Pre Calculus

Question

Which of the answer choices has matrix multiplication defined?

A B C D
⌈1 2⌉ ⌈5 6 7⌉ ⌈-1 2 3⌉ [5 9 7]

⌊3 4⌋ ⌊8 9 0⌋ l8 -4 0l

..................⌊6 7 1⌋

a) AC
b) BA
c) AB
d) CD

Answer 1

dimensions of A : 2x2 (number of rows x numbers of columns)

dimensions of B : 2x3

dimensions of C : 3x3

dimensions of D : 1x3

 

In order for a matrix multiplication to be defined the 'inside' numbers of their dimensions need to be the same:

 

AB: 2x2<-  ->2x3 : the inside numbers are both 2's so the matrix multiplication is defined

 

AC: 2x2<-   ->3x3 : the inside numbers do not match (a 2 for A and a 3 for C) so the matrix multiplication is not defined

 

BA: 2x3<-   ->2x2 : the inside numbers do not match (a 3 for B and a 2 for A) so the matrix multiplication is not defined

 

CD: 3x3<-  ->1x3 : the inside numbers do not match (a 3 for C and a 1 for D) so the matrix multiplication is not defined